Finding a generating function

Here's the problem:

Let be a generating function for the sequence . Find a sequence whose generating function is .

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We know that, given a sequence , the generating function of that sequence is .
Let's define and it is known that is a generating function for the sequence , i.e. .
Therefore we have the relationship and I'm a little lost finding what exactly is .

Let be a generating function for the sequence . Find a sequence whose generating function is .

***

We know that, given a sequence , the generating function of that sequence is .
Let's define and it is known that is a generating function for the sequence , i.e. .
Therefore we have the relationship and I'm a little lost finding what exactly is .